WASHINGTON, July 17 (Reuters) - With time running short in U.S. debt talks, Republican and Democratic senators sought on Sunday to craft a plan that could avert an unprecedented government default while making modest cuts in the deficit.

Aides to President Barack Obama said he still holds out hope for a “grand bargain” that would combine a deal for up to $4 trillion in deficit reduction with an agreement to raise the country’s borrowing limit.

But there were few signs of progress as the Aug. 2 deadline to avoid a default drew dangerously close.

Behind the scenes, Senate Republican leader Mitch McConnell and Senate Democratic leader Harry Reid were negotiating over a fallback plan proposed by McConnell that would allow Obama to raise the debt limit while sparing Republicans from having to vote in favor of it.

Senior Democratic aides said the U.S. Senate will likely begin considering the compromise measure this week. They predicted the Democratic-led Senate would pass the legislation, but winning over the Republican-led House of Representatives would pose a bigger challenge.

“Barring a breakthrough, this is going to be the plan,” one congressional aide said. “We are working under the assumption that there won’t be a (deficit) plan.”

Making the rounds on the Sunday morning talk shows, White House budget director Jack Lew told CNN’s “State of the Union” program he believed that all of the leaders in Congress “understand it would be irresponsible to get to Aug. 2” and not have a debt-limit increase.

If Congress does not raise the $14.3 trillion limit on U.S. borrowing by then, the government will run out of money to meet all it’s payments. Economists and administration officials have warned this would trigger a crisis in global financial markets and plunge the United States into another recession.

Obama’s quest for a debt-limit increase and a $4 trillion deficit reduction deal hit a major obstacle a week ago when Republicans in Congress rejected his demand that tax increases on the wealthy be part of the plan.

“PLAN B”

Lew told NBC’s “Meet the Press” that there was still time to achieve a far-reaching deal. “The president has made it clear he wants to do something substantial,” he said.

But a growing number of private-sector experts believe the solution to the debt standoff might lie in the “Plan B” sketched out by McConnell.

That proposal would involve a convoluted legislative maneuver to raise the debt limit in three stages. It would put the burden on Obama’s Democrats to approve the increase, but, in its initial form, it would not require spending cuts.

Reid is seeking some changes to make the plan more palatable to Democrats, including a requirement of up to $1.5 trillion in spending cuts. The cuts would consist of those identified by a deficit-reduction group headed by Vice President Joe Biden. Aides to McConnell and Reid have also discussed creating a bipartisan panel on deficit reduction.

Still, the idea could be a tough sell in the Republican-led House where it has been greeted coolly by conservative Tea Party activists.

Obama had set a weekend deadline for an action plan from the lawmakers and said he might call them back for further White House talks. But there were no meetings over the weekend. As of Sunday evening, no talks were planned for Monday.

“Conversations have continued throughout the weekend, but there is no news or progress to report,” said Michael Steel, a spokesman for House Speaker John Boehner, the top U.S. Republican. Boehner has scheduled a vote for Tuesday on his “cut, cap and balance” plan that would condition an increase in the debt-limit on passage of a constitutional amendment to require the federal government to balance its books each year.

That bill stands little chance of passing the Senate but it might buy some goodwill with conservatives to eventually allow for passage of a compromise, such as the McConnell plan.

State governors, fearing the effects of the debt talks on their own credit ratings, have pressured Washington to get a deal. [ID:nN1E76F07A]

At a meeting of the nation’s governors in Salt Lake City, Utah, Washington Governor Christine Gregoire said they agreed the debt limit should be increased.

“We’re getting hurt by the inaction of what’s going on in Washington D.C.,” Gregoire, chairwoman of the National Governors Association, told Reuters.

Mississippi Governor Haley Barbour, a Republican, said that as far as he knew, all of the governors present thought the debt ceiling needed to be raised but there were differences on what the legislation should look like. “There are people like me who think raising taxes would be very harmful to the economy,” Barbour said. (Additional reporting by Alina Selyukh and Donna Smith in Washington and Edith Honan in Salt Lake City. Writing by Caren Bohan; Editing by Christopher Wilson)